Some extremely amenable groups

dc.creatorGiordano, Thierry
dc.creatorPestov, Vladimir
dc.date2001-09-19
dc.date2001-10-27
dc.date.accessioned2026-07-07T08:26:58Z
dc.date.available2026-07-07T08:26:58Z
dc.descriptionA topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe's result, we show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact group.
dc.description7 pages, English with abridged French version
dc.identifierhttps://arxiv.org/abs/math/0109138
dc.identifierhttp://arxiv.org/abs/math/0109138
dc.identifierC.r. Acad. Sci. Paris, Ser. I 334 (2002), No. 4, 273-278.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137122
dc.subjectGroup Theory
dc.subjectDynamical Systems
dc.subjectOperator Algebras
dc.subject43A07; 37A15; 46L10
dc.titleSome extremely amenable groups
dc.typetext

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